Metachronal waves in concentrations of swimming Turbatrix aceti nematodes and an oscillator chain model for their coordinated motions

Abstract

At high concentration, free swimming nematodes known as vinegar eels (Tubatrix aceti), collectively exhibit metachronal waves near a boundary. We find that the frequency of the collective traveling wave is lower than that of the freely swimming organisms. We explore models based on a chain of oscillators with nearest neighbor interactions that inhibit oscillator phase velocity. The phase of each oscillator represents the phase of the motion of the eel's head back and forth about its mean position. A strongly interacting directed chain model mimicking steric interactions between organisms robustly gives traveling wave states and can approximately match the observed wavelength and oscillation frequency of the observed traveling wave. We predict body shapes assuming that waves propagate down the eel body at a constant speed. The phase oscillator model that impedes eel head overlaps also reduces close interactions throughout the eel bodies.

Collective behaviour of swarmalators on a 1D ring

“…Vinegar eels are a type of nematode found in beer mats and the slime from tree wounds [13,14]. They can be considered swarmalators because they sync the wriggling of their heads, swarm in solution, and it seems likely based on their behavior said sync and swarming interact [13,14] (neighbouring eels sync more easily than distant eels, so sync interacts with swarming, and sync'd eels presumable affect each local hydrodynamic environment and thereby affect each other's movements, so swarming interacts with sync).…”

“…Vinegar eels are a type of nematode found in beer mats and the slime from tree wounds [13,14]. They can be considered swarmalators because they sync the wriggling of their heads, swarm in solution, and it seems likely based on their behavior said sync and swarming interact [13,14] (neighbouring eels sync more easily than distant eels, so sync interacts with swarming, and sync'd eels presumable affect each local hydrodynamic environment and thereby affect each other's movements, so swarming interacts with sync). When confined to 2D disks, they seek out the 1D ring boundary forming metachronal waves in which the phase of their gait and their spatial positions around the ring are splayed similar to the static phase wave [13,14] (although note the winding number for the metachronal waves is k > 1; a full rotation in physical space x produces k > 1 rotations in phase θ).…”

“…[76] https://github.com/Khev/swarmalators/blob/master/1D/onring/regular/stability-static-phase-wave.nb [77] We say 'appear' to meet these definition because what is means to prove a bidirectional space-phase coupling in an experimental system is somewhat ambiguous. Most experimental studies of swarmalators either infer a spacephase coupling exists based on the observations (like the microswimmers [11,13,62] we describe; [62] do a particularly comprehensive study), but do not specify if the coupling bidirectional. Other studies demonstrate a twoway coupling in the sense that they encoding it in a model that produces behavior similar to observed data (like magnetic domain walls [32] or myxobacteria [68]).…”

“…The units of some systems appear to self-organize in both space and time. In Biology, sperm [11,12], vinegar eels [13,14], and other microswimmers [15][16][17] synchronize the wriggling of their tails which is speculated to hydrodynamically couple to their motion. In Chemistry, magnetic Janus particles [18][19][20], dieletric Quinke rollers [21][22][23], and other active entities [24] lock their rotations enabling a kind of sync-dependent self-assembly.…”

Lateral contact yields longitudinal cohesion in active undulatory systems

“…This work is inspired by recent observations of collective undulatory swimming in nematodes [46], vinegar worms [47,48], and sperm. These undulatory swimmers often form clusters of high-density swimmers [17,49], and the close-proximity between individuals can generate forceful interactions through hydrodynamics and contact.…”